| In the study of the fuzzy system and fuzzy control theory, the construction of fuzzy system and its universal approximation is one of the research issues. As the core of fuzzy control systems, fuzzy inference is becoming an important research issues.In the construction of a fuzzy system, most of the literatures deal with the input variables by singleton fuzzifier and the fuzzy inference method is CRI or triple I method and the center average method is also adopted in defuzzification. The paper adopts a new fuzzy inference of double I algorithm which constructs a new fuzzy system by non-singleton fuzzifier and center of gravity defuzzifier. The main content is as follows:First, introduce the development of fuzzy system theory. This party mainly introduces what is fuzzy system and the development of the fuzzy system, the research significance of fuzzy system is also presented.Second, it proposes the concept of double I algorithm on the basis of CRI and triple I algorithm. This section introduces concept of double I algorithm and makes a study its properties, including its geometric significance, monotonicity, continuity and reduction. Then the three fuzzy inference algorithms are compared in terms of these properties,Third, it constructs a SISO fuzzy system based on double I algorithm. This paper constructs several fuzzy systems with some regular fuzzy implication operators, in the same time the universal approximation of fuzzy systems is analyzed and the simulation results are given.It shows that the fuzzy system is universal approximator with first-order approximation accuracy.Finally, it represents the probability of the SISO fuzzy system based on double I algorithm and points out the corresponding probability density distribution and specific expression of the digital characteristics. The results show the relationship between fuzzy system and probability theory,it also pointes out that the center of gravity defuzzifier method is most optimal method in the sense of mean square. |
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